Reduced Z-Buffer Generating Method, Hidden Surface Removal Method and Occlusion Culling Method

ABSTRACT

A rendering processing apparatus is provided which performs occlusion culling for excluding from rendering targets a hidden object behind another object as seen from a point of view, when given a plurality of objects. An object input unit stores a plurality of objects in an object storing unit. An internal volume generating unit generates an internal volume which is included in a target object. A reduced Z-buffer updating unit updates a reduced Z-buffer based on the internal volume. An external volume generating unit generates an external volume which includes the target object subject to culling test. A culling determination unit consults the reduced Z-buffer and performs a Z culling test on the target object based on the external volume.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a reduced Z-buffer generating technology, ahidden surface removal technology, an occlusion culling technology, anda rendering processing technology in computer graphics.

2. Description of the Related Art

When rendering three-dimensional objects in 3D computer graphics, ahidden surface removal process is performed to remove hidden surfacesbehind other objects. Z-buffer method is one of typical techniques forthe hidden surface removal process. In the Z-buffer method, the hiddensurface removal process is performed by: retrieving the per-pixel Zvalue from a Z-buffer which contains Z values or depth information pixelby pixel on screen; and rendering a target pixel to be processed if thepixel lies in front of the position indicated by the correspondingper-pixel Z value, and canceling rendering processing for the targetpixel if the pixel lies behind the position.

The Z-buffer method requires as much memory capacity as that of a framebuffer which stores the color values of the pixels. The frame bufferwill not be accessed where target pixels subject to hidden surfaceremoval are concerned, since the pixel values of those pixels need notbe written. The Z-buffer, on the other hand, must be consulted for Zvalues to perform a Z test even on pixels that end up being subjected tohidden surface removal, thus resulting in a higher processing cost.

Since the Z-buffer method requires a large memory capacity and a highprocessing cost, various ideas have recently been devised to reduce thecost involved in the hidden surface removal process as much as possible.For example, occlusion culling is performed to select a hidden objectbehind the other objects and exclude it from rendering targets inadvance. The occlusion culling makes it possible to choose renderingtargets on a per-object or per-polygon basis for the purpose ofreduction at an earlier stage prior to a rasterization process.

Moreover, an early Z culling may be performed to remove hidden andinvisible fragments at the stage of generating fragments prior to pixelprocessing. A hierarchical Z culling may also be performed, which uses ahierarchical Z-buffer including different resolutions of Z-buffersstacked hierarchically. These techniques make the hidden surface removalprocess more efficient.

One of the occlusion culling methods is to form a bounding volume aroundan object so as to include the object, and exclude the object fromrendering targets if its bounding volume is entirely hidden behind thebounding volumes of the other objects. This requires the computation,prior to rasterization process, to detect whether or not a boundingvolume is entirely hidden behind the other bounding volumes on screencoordinates. The occlusion culling process increases in difficulty asthe recent 3D graphics utilizes an enormous number of objects to berendered and the positional relationship between the objects is morecomplicated.

The Z culling using a hierarchical Z-buffer also leads to a highcomputation cost. The generation of the hierarchical Z-buffer requiresthe process for providing a per-pixel Z-buffer and then reducing itsresolution stepwise so as to generate Z-buffers having the differentresolutions.

SUMMARY OF THE INVENTION

The present invention has been achieved in view of the foregoingproblems, and a general purpose thereof is to provide a renderingprocessing technology capable of enhancing the efficiency of renderingprocessing according to the positional relationship of a plurality ofthree-dimensional objects in a depth direction.

To solve the foregoing problems, one embodiment of the present inventionprovides a reduced Z-buffer generating method. The method includes:providing a reduced Z-buffer which contains representative Z values fordetermining a positional relationship between plural objects orfragments constituting the objects in a depth direction, therepresentative Z values indicating a depth from the point of view inunits of predetermined pixel blocks each including a plurality ofneighboring pixels; and comparing the Z values of respective rasterizedpixels in a pixel block of an object or a fragment to be rendered withthe representative Z value of a corresponding pixel block stored in thereduced Z-buffer, and updating the representative Z value of the pixelblock with a farthest Z value if the farthest Z value indicates lyingcloser to the point of view than the representative Z value of the pixelblock does, the farthest Z value indicating lying the farthest from thepoint of view among the per-pixel Z values in the pixel block.

Yet another embodiment of the present invention provides an occlusionculling method for excluding from rendering targets a hidden objectbehind another objects as seen from a point of view, when given aplurality of objects. The method includes: providing a reduced Z-bufferwhich contains representative Z values for determining a positionalrelationship between the objects in a depth direction, therepresentative Z values indicating a depth from the point of view inunits of predetermined pixel blocks each including a plurality ofneighboring pixels; comparing the Z values of respective rasterizedpixels in a pixel block of an object to be rendered with therepresentative Z value of a corresponding pixel block stored in thereduced Z-buffer, and updating the representative Z value of the pixelblock with a farthest Z value if the farthest Z value indicates lyingcloser to the point of view than the representative Z value of the pixelblock does, the farthest Z value indicating lying the farthest from thepoint of view among the per-pixel Z values in the pixel block; anddetermining that the object has a possibility of being rendered if itturns out that at least one of the pixel blocks of the object to berendered has any rasterized pixel having a Z value that indicates lyingcloser to the point of view than the representative Z value of acorresponding pixel block stored in the Z-buffer does.

Yet another embodiment of the present invention provides a hiddensurface removal method for removing a hidden surface behind anotherobject as seen from a point of view, when given a plurality of objects.the method includes: providing a reduced Z-buffer which containsrepresentative Z values for determining a positional relationshipbetween fragments constituting the plurality of objects in a depthdirection, the representative Z values indicating a depth from the pointof view in units of predetermined pixel blocks each including aplurality of neighboring pixels; comparing the Z values of respectiverasterized pixels in a pixel block of a fragment to be rendered with therepresentative Z value of a corresponding pixel block stored in thereduced Z-buffer, and updating the representative Z value of the pixelblock with a farthest Z value if the farthest Z value indicates lyingcloser to the point of view than the representative Z value of the pixelblock does, the farthest Z value indicating lying the farthest from thepoint of view among the per-pixel Z values in the pixel block; anddetermining that the fragment has the possibility of being rendered ifit turns out that at least one of the pixel blocks of the fragment to berendered has any rasterized pixel having a Z value that indicates lyingcloser to the point of view than the representative Z value of acorresponding pixel block stored in the Z-buffer does.

It should be appreciated that any combinations of the foregoingcomponents, and any conversions of expressions of the present inventionfrom/into methods, apparatuses, systems, computer programs, datastructures, and the like are also intended to constitute applicableembodiments of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings which are meant to be exemplary,not limiting, and wherein like elements are numbered alike in severalFigures, in which:

FIG. 1A illustrates an object given as a rendering target, and FIG. 1Billustrates an external volume and an internal volume provided for theobject;

FIG. 2 illustrates another example of an external volume and an internalvolume provided for an object;

FIG. 3 shows a reduced Z-buffer;

FIG. 4 shows the relationship between a polygon of an external volume ofan object and a reduced Z-buffer;

FIG. 5 shows the relationship between a representative Z value andper-pixel Z values in a pixel block of the reduced Z-buffer of FIG. 4;

FIG. 6A shows another example of the relationship between arepresentative Z value and the per-pixel Z values in a pixel block ofthe reduced Z-buffer of FIG. 4;

FIGS. 6B and 6C show examples of pixel-by-pixel distribution of Z valuesin the pixel block of FIG. 6A;

FIG. 7 explains how rasterization process and Z test is performed on twopixel blocks of the reduced Z-buffer of FIG. 4 in sequence;

FIG. 8 shows sampling points on which Z test is performed in the processof rasterizing a polygon of an external volume;

FIG. 9 shows the relationship between polygons of a projected internalvolume and a reduced Z-buffer;

FIG. 10 shows the values of determination flags set on the respectiveedges of the polygons of the internal volume shown in FIG. 9;

FIGS. 11A to 11C show polygon edges that pass through three pixel blocksof the reduced Z-buffer of FIG. 9, along with the values of theirdetermination flags of FIG. 10;

FIG. 12 explains how a representative Z value of a pixel block of areduced Z-buffer is updated;

FIG. 13 shows sampling points subject to a Z test in rasterizing thepolygons of the internal volume;

FIGS. 14A and 14B show a front board and a rear board provided for anobject;

FIG. 15 is a block diagram of a rendering processing apparatus accordingto an embodiment;

FIG. 16 is a block diagram of the Z culling processing unit of FIG. 15;

FIG. 17 is a block diagram of the rendering processing unit of FIG. 15;

FIG. 18 is a flowchart for explaining the procedure of Z cullingprocessing to be performed by the Z culling processing unit of FIG. 16;

FIG. 19 is a flowchart showing the procedure of culling test performedby the culling determination unit of FIG. 16; and

FIG. 20 is a flowchart showing the procedure performed by the reducedZ-buffer updating unit of FIG. 16 for updating a reduced Z-buffer.

DETAILED DESCRIPTION OF THE INVENTION

The invention will now be described by reference to the preferredembodiments. This does not intend to limit the scope of the presentinvention, but to exemplify the invention.

An overview will now be given of an embodiment of the present invention.When given a set of objects to be rendered, the embodiment provides anocclusion culling method for excluding from rendering targets a hiddenobject behind the other objects when seen from a point of view. Thefollowing means will be used for the occlusion culling according to theembodiment.

(1) A reduced Z-buffer which contains representative Z values fordetermining a positional relationship between the objects in a depthdirection. The representative Z value indicates a depth from the pointof view in units of pixel blocks each of which contains a plurality ofneighboring pixels.

(2) An external volume and an internal volume. When given a targetobject to be determined whether or not there is any possibility of beingactually rendered, the external volume includes the target objecttherein and the target object includes the internal volume therein.

The representative Z values of the reduced Z-buffer are updated usingthe internal volume as follows. The per-pixel Z values in a pixel blockof the internal volume to be rendered are compared with therepresentative Z value of a corresponding pixel block stored in thereduced Z-buffer. If the largest value among the per-pixel Z valueswithin the pixel block is smaller than the representative Z value of thepixel block, the representative Z value of the pixel block is updatedwith the largest per-pixel Z value in the pixel block.

A test for the object culling is performed using the reduced Z-bufferbased on the external volume as follows. It is determined that theobject has a possibility of being rendered if it turns out that at leastone of pixel blocks of the external volume to be rendered has any oneper-pixel Z value that is smaller than the per-pixel-blockrepresentative Z value of the corresponding pixel block stored in thereduced Z-buffer. Conversely, the object is excluded from renderingtargets and culled out if the smallest per-pixel Z value within everypixel block of the external volume to be rendered is greater than theper-pixel-block representative Z value of the corresponding pixel blockstored in the reduced Z-buffer.

In this way, an object subject to the rendering test is provided withtwo bounding volumes, i.e., the external volume and the internal volume,and the per-pixel Z values of those volumes and the per-pixel-blockrepresentative Z value of the reduced Z-buffer are compared for thehidden surface removal process. Consequently, objects that will not berendered are screened out in advance, so that only those having thepossibility of being rendered are rasterized for subsequent renderingprocessing. This speeds up the entire rendering processing.

Hereinafter, the setting up of the external volume and the internalvolume, the Z culling using the external volume and the reducedZ-buffer, and the updating of the reduced Z-buffer using the internalvolume will now be described in detail.

[1] External Volume and Internal Volume

FIG. 1A illustrates an object 200 given as a rendering target. FIG. 1Billustrates an external volume 400 and an internal volume 300 providedfor the object 200. The external volume 400 is formed so as to entirelyinclude the object 200 therein. The internal volume 300 is formed so asto be entirely included inside the object 200.

For example, the external volume 400 is a rectangular solid having theminimum size required to entirely include the object 200. The internalvolume 300 is a rectangular solid having the maximum size required to beentirely included inside the object 200. Alternatively, the externalvolume 400 and the internal volume 300 may be a solid body having ashape other than a rectangular solid, such as a sphere. The externalvolume 400 and the internal volume 300 may be a closed space that issurrounded by polygons each having an external volume attribute and aninternal volume attribute, respectively.

The external volume 400 may also be referred to as an “inclusion volume”since it includes the object 200 within its inside. The internal volume300 may also be referred to as an “exclusion volume” since it excludesthe surfaces of the object 200 to its outside. The external volume 400delimits from outside the space for the object 200 to occupy, while theinternal volume 300 delimits from inside the space for the object 200 tooccupy. In that sense, the external volume 400 and the internal volume300 can be regarded as “double bounding volumes” which define the shapeof the object 200 from both outside and inside.

The external volume 400 is used when consulting the reduced Z-buffer andperforming a Z test to determine if the object 200 included therein hasthe possibility of being rendered, i.e., whether or not to exclude (cullout) the object from rendering targets. The external volume 400 is notused to update Z values of the reduced Z-buffer. On the other hand, theinternal volume 300 is used to update representative Z values in thereduced Z-buffer but not for the culling test on the object 200.

The external volume 400 and the internal volume 300 may have any shapesand any complexities as long as they are capable being rasterized. Thesetwo bounding volumes are provided for reducing the number of polygons ofthe object 200 so as to reduce a required memory capacity and toaccelerate the Z culling test and the updating of the reduced Z-buffer.As described later, there is a guarantee that the object 200 will not beerroneously culled out even though the Z culling is performed based onthe external volume 400 while the representative Z values of the reducedZ-buffer is being updated based on the internal volume 300.

It should be noted that either one or both of the external volume 400and the internal volume 300 can be equal to the object 200. That is, theZ culling test and/or the updating of the reduced Z-buffer may beperformed by simply using the surficial shape of the object 200 as theexternal volume 400 and/or the internal volume 300. In this case, sincethe external and/or internal volumes have the same shape as the object200 with a greater number of polygons, there will be an increase in boththe memory capacity and the amount of calculation. However, it canincrease accuracy in determining and culling out more objects that haveno possibility of being rendered.

The closer to the shape of object 200 the external volume 400 and/or theinternal volume 300 are formed, the greater the number of objects thatcan be culled out becomes. However, the required amount of memory andcalculation will increase. On the other hand, the simpler the shape ofthe external volume 400 and/or the internal volume 300, the less theamount of memory and calculation. However, the number of objects thatcan be culled out will decrease. There is thus a tradeoff between thenumber of objects that can be culled out and the amount of memory andcalculation required. Therefore the shape of the external volume 400and/or the internal volume 300 will be determined appropriately inconsideration of the balance between culling efficiency and limitationsin the memory capacity and the processing performance of the computer.

FIG. 2 illustrates the external volume 410 and the internal volume 310provided for the object 200, as another example. The external volume 410is a cylinder which includes the object 200 therein. The internal volume310 is composed of two orthogonal plates which are included inside theobject 200. The internal volume 310 need not be an object having solidcontents, but may be made of plates such as these having no thickness.For the sake of convenience, the term “volume” will still be used evenfor the plates having no thickness.

The internal volume 310 has two plates in a cross-like shape when viewedfrom above. However, it may be made of three or more plates, or a singleplate in some cases. In the case of a single plate, however, theinternal volume 310 may look thinner or even disappear completelydepending on the point of view. After projection transformation, thearea occupied by the internal volume 310 might therefore shrink so thatthe reduced Z-buffer cannot be adequately updated. However, when twoplates are crossed each other, it prevents the internal volume 310 fromdisappearing depending on the point of view, and reduces the amount ofcalculation as compared to when three or more plates are used. Theinternal volume 310 is thus more preferably composed of two orthogonalplates.

[2] Z Test

The external volume 400 and the internal volume 300, provided for theobject 200, are each composed of polygons. These polygons are projectedonto screen coordinates where the object 200 is rendered, followed byrasterization processing corresponding to the reduced Z-buffer. Therasterization of the external volume 400 involves a Z culling test usingthe reduced Z-buffer. The rasterization of the internal volume 300involves updating the representative Z values of the reduced Z-buffer.

[2.1] Reduced Z-Buffer

FIG. 3 shows a reduced Z-buffer 500. The reduced Z-buffer 500 is abuffer of reduced resolution, having pixel blocks where a plurality ofpixels given in a tile shape in the Z-buffer used for rendering aregrouped. Since the two bounding volumes, or the external volume 400 andthe internal volume 300, are rasterized in association with the reducedZ-buffer 500, it is possible to perform hidden surface removal with aless amount of processing.

In the example of FIG. 3, the reduced Z-buffer 500 stores Z values inunits of pixel blocks each having a 4 by 4 matrix of pixels. In thediagram, the minimum pixels are bordered by dotted lines, and the pixelblocks by solid lines. One pixel block includes 16 pixels. Theper-pixel-block Z value is referred to as a “representative Z value.”The Z value herein indicates depth as seen from the point of view. The Zvalue decreases in a direction of approaching toward the point of viewand increases in a direction of leaving away from the point of view.

The representative Z value of each pixel block in the reduced Z-buffer500 is determined according to the following three types of per-pixel Zvalues: the Z values of pixels at the vertexes of polygons of theinternal volume 300 that are rendered in this pixel block; the Z valuesof pixels at intersections between the edges of those polygons and theborders of this pixel block; and the Z values of pixels at four cornersof this pixel block. It is ensured that the representative Z value ofeach pixel block is the largest value among the per-pixel Z values inthe pixel block, i.e., the Z value of the pixel that is farthest fromthe point of view. The method for updating the representative Z valuesin the reduced Z-buffer 500 will be described later.

[2.2] Z Culling Test Using the Reduced Z-Buffer Based on the ExternalVolume

The external volume 400 is provided for detecting areas where the object200 has the possibility of being rendered, and for determining whetheror not to cull out the object 200. The object 200 must not be culled outif there is any area where the possibility of being rendered cannot bedenied. To guarantee that there is no area missed in the culling test,the external volume 400 has to include the object 200 entirely. Evenwhen the external volume 400 has any redundant area that is notspatially occupied by the object 200, the culling test can be performedwithout any failure, although the processing efficiency may drop.

In the rasterization process of the external volume 400, a Z cullingtest is made as follows. It is determined that the object 200 has apossibility of being rendered if it turns out that at least one of pixelblocks of the external volume 400 to be rendered has any one per-pixel Zvalue that is smaller than the representative Z value of thecorresponding pixel block in the reduced Z-buffer 500. Conversely, theobject 200 is culled out if the smallest per-pixel Z value within everypixel block of the external volume to be rendered is greater than therepresentative Z value of corresponding pixel block in the reducedZ-buffer.

For each pixel block, the Z value of the closest pixel is thus comparedwith the representative Z value of the reduced Z-buffer 500 so that itcan be reliably determined that the object 200 having a possibility ofbeing rendered is a rendering target. Therefore there is a guaranteethat any object 200 that has a possibility of being rendered never beerroneously culled out. The rasterization process of the external volume400 involves the Z culling test alone. In other words, therepresentative Z values of the reduced Z-buffer 500 are referred to andcompared with the per-pixel Z values, however, no representative Z valuewill be written to the reduced Z-buffer 500. Hereinafter, the procedureof the Z culling test will now be described with reference to someconcrete examples.

FIG. 4 shows the relationship between a polygon 402 of the externalvolume 400 of the object 200 and the reduced Z-buffer 500. The figureshows the polygon 402 projected onto the drawing plane. The polygon 402will be rendered in the pixel blocks (reference numerals 502, 504 and soon) shown shaded in the reduced Z-buffer 500. The polygon 402 israsterized and the Z values of the pixels are calculated. Then theper-pixel Z values are compared with the representative Z value of thecorresponding pixel block for Z test.

FIG. 5 shows the relationship between the representative Z value and theper-pixel Z values in the pixel block 502 of the reduced Z-buffer 500 ofFIG. 4. The pixel block 502 has a representative Z value of Zr=15. Thevertex B of the polygon 402 has a Z value of b=20. The intersections C1and C2 between the edges of the polygon 402 and the borders of the pixelblock 502 have Z values of c1=25 and c2=24, respectively. Among the fourcorners of the pixel block 502, the point D that falls within thepolygon 402 has a Z value of d=26.

In the case of FIG. 5, the pixels in the pixel block 502, obtained byrasterizing the polygon 402, have Z values greater than therepresentative Z value of this pixel block 502 in the reduced Z-buffer500. It is therefore certain that the polygon 402 lies behind thereduced Z-buffer 500 as far as the pixel block 502 is concerned. This isbecause the pixel block 502 of the reduced Z-buffer 500 has therepresentative Z value of Zr=15, and it is ensured by the definition ofthe reduced Z-buffer 500 that this representative Z value is the largestamong the Z values of the pixel block 502 when it is viewed in a unit ofthe minimum pixel. Since the Z values of the minimum pixels of the pixelblock 502 do not exceed 15, it is clear that the points B, C1, C2, and Don the polygon 402, sampled within the pixel block 502, definitely liebehind.

The Z test is performed on every pixel block shown shaded in FIG. 4where the polygon 402 is to be rendered. If for the every pixel blockthe Z values of the rasterized pixels are greater than therepresentative Z value of the reduced Z-buffer 500, it turns out thatthe polygon 402 must be subject to hidden surface removal. The Z test isperformed on all the polygons of the external volume 400 to be rendered,and if it turns out that all the polygons must be subject to hiddensurface removal, then it is finally determined that the external volume400 is invisible from the point of view. In this case, the object 200included inside the external volume 400 is culled out.

FIG. 6A shows another example of the relationship between therepresentative Z value and the per-pixel Z values in the pixel block 502of the reduced Z-buffer 400 of FIG. 4. In this example, the pixel block502 has a representative Z value of Zr=15. The vertex B of the polygon402 has a Z value of b=10. The intersections C1 and C2 between the edgeof the polygon 402 and the borders of the pixel block 502 have Z valuesof c1=40 and c2=30, respectively. The corner D of the pixel block 502inside the polygon 402 has a Z value of d=34.

In the case of FIG. 6A, the Z value b at the vertex B is smaller thanthe representative Z value (Zr=15) of the pixel block 502 of the reducedZ-buffer 500. The Z values c1 and c2 at the intersections C1 and C2 andthe Z value d at the corner D of the pixel block 502 in the polygon 402are greater than the representative Z value of the pixel block 502.Here, it is uncertain whether or not the polygon 402 lies in front orbehind at the pixel block 502 unless the Z values are compared in a unitof the minimum pixel. FIGS. 6B and 6C show examples of pixel-by-pixeldistribution of Z values in the pixel block 502. With the reference toFIGS. 6B and 6C, it will be now determined for the respectivepixel-by-pixel distribution whether or not the polygon 402 lies in frontor behind at the pixel block 502.

FIG. 6B shows an example of distribution of the per-pixel Z values inthe pixel block 502. The vertex B has a Z value of b=10 that is greaterthan the per-pixel Z value or 8 in the same position. The vertex B thuslies behind. In this case, the vertex B, the intersections C1 and C2,and the corner D are all positioned behind. It turned out that thispolygon 402 lies behind as far as the pixel block 502 is concerned.

FIG. 6C shows another example of distribution of the per-pixel Z valuesin the pixel block 502. The vertex B has a Z value of b=10 that issmaller than the per-pixel Z value or 15 in the same position. Thevertex B thus lies in front. Since at least the vertex B of the polygon402 lies in front, the polygon 402 must be determined to be a renderingtarget and the object 200 must not be culled out.

According to the discussion referring to FIG. 5 and FIGS. 6A to 6C, thefollowing can be understood. It must be determined based on a relaxedcriterion such as “when in doubt, render it” whether or not the polygon402 has a possibility of being rendered. On the other hand, it must bedetermined based on a rigid criterion such as “when in doubt, do notcull it out” whether or not to exclude the polygon 402 from renderingtargets and cull it out.

In order to guarantee that any object having a possibility of beingrendered is not erroneously culled out, a rigid culling criterion isdefined as follows.

[Rigid Culling Criterion B]

For every pixel block where the external volume 400 is to be rendered,cull out the object 200 only if all the rasterized pixels to be renderedwithin the pixel block have Z values greater than the representative Zvalue of that pixel block of the reduced Z-buffer 500, or equivalently,cull out the object 200 if the smallest value among the Z values of therasterized pixels to be rendered within the pixel block is greater thanthe representative Z value of that pixel block of the reduced Z-buffer500.

When comparing the per-pixel Z values within the pixel block 502 wherethe polygon 402 of the external volume 400 is to be rendered and therepresentative Z value of the pixel block 502 of the reduced Z-buffer500, it is unnecessary to compare every pixel obtained from therasterized polygon 402 with the representative Z value of the pixelblock 502. Instead, it will be sufficient to only evaluate the Z valuesat the endpoints of the polygon 402 since the polygon 402 is atwo-dimensional surface. More specifically, as described with referenceto FIGS. 5 and 6A, what must be compared with the representative Z valueZr of the pixel block 502 are the following three types of Z values: theZ value b of the pixel at the vertex B of the polygon 402 of theexternal volume 400 falling within the pixel block 502; the Z values c1and c2 of the pixels at the intersections C1 and C2 between the edges ofthe polygon 402 and the borders of the pixel block 502; and the Z valued of the pixel at the corner D of the pixel block 502 inside the polygon402. Consequently, the rigid culling criterion B can be simplified asfollows.

[Rigid Culling Criterion B′]

For every pixel block where the external volume 400 is to be rendered,cull out the object 200 if b>Zr and c>Zr and d>Zr, or equivalently, cullout the object 200 if min(b, c, d)>Zr. Here, b is the Z value at avertex B of the polygon of the external volume 400 falling within thepixel block, c is the Z value at an intersection C between an edge ofthe polygon and a border of the pixel block, and d is the Z value at acorner D of the pixel block inside this polygon. If there are pluralvertexes B, intersections C, or corners D, all the sampling points aresubject to the evaluation.

The rigid culling criterion B′ is such that for every pixel block wherethe external volume 400 is to be rendered, the object is culled out onlyif the nearest point among vertexes B, intersections C, and corners Dlies behind the position indicated by the representative Z value Zr ofthe reduced Z-buffer 500. By the definition of the reduced Z-buffer 500,none of the Z values in a unit of the minimum pixel exceeds therepresentative Z value Zr of the reduced Z-buffer 500. It is guaranteedthat any object to be rendered will not be erroneously culled out aslong as culling is performed based on this criterion.

The logical negation of the rigid culling criterion B provides a relaxedrendering criterion that is “when in doubt, render it” as follows.

[Relaxed Rendering Criterion A]

It is determined that the object 200 has a possibility of being renderedif it turns out that at least one of pixel blocks where the externalvolume 400 is to be rendered has any one per-pixel Z value that issmaller than the representative Z value of that pixel block of thereduction Z-buffer 500.

Since the polygon 402 of the external volume 400 is a two-dimensionalplane, the relaxed rendering criterion A can be simplified as follows.

[Relaxed Rendering Criterion A′]

For at least one of pixel blocks where the external volume 400 is to berendered, it is determined that the object 200 has a possibility ofbeing rendered if b<Zr or c<Zr or d<Zr. Here, b is the Z value at avertex B of the polygon of the external volume 400 falling within thepixel block, c is the Z value at an intersection C between an edge ofthe polygon and a border of the pixel block, and d is the Z value at acorner D of the pixel block inside this polygon. If there are pluralvertexes B, intersections C, or corners D, all the sampling points aresubject to the evaluation.

Once the relaxed rendering criterion A′ holds for any one pixel block inthe process of rasterizing the external volume 400 of the object 200 forZ test, then it is immediately determined that the object 200 has apossibility of being rendered and the Z culling test proceeds to thenext object for the sake of accelerating the process. If the relaxedrendering criterion A′ does not hold for any of the pixel blocks wherethe external volume 400 of the object 200 is to be rendered, then therigid culling condition B′ holds consequently and the object 200 isculled out.

FIG. 7 explains how rasterization process and Z test is performed on thetwo pixel blocks 502 and 504 of the reduced Z-buffer 500 of FIG. 4 insequence. First, the left pixel block 502 of the reduced Z-buffer 500 israsterized. The vertex B of the polygon 402 has a Z value of b=20. Theintersections C1 and C2 have Z values of c1=18 and c2=16, respectively.The corner D1 has a Z value of d1=14. The left pixel block 502 has arepresentative Z value of Zr=7. In the left pixel block 502, all thesampling points B, C1, C2, and D1 inside the polygon 402 have Z valuesgreater than the representative Z value and thus lie behind. At thestage of rasterizing the left pixel block 502, it is therefore not yetdetermined that the object 200 has a possibility of being rendered.

Next, the rasterization processing proceeds to the right pixel block504. In the right pixel block 504, the intersections C1 and C3 of thepolygon 402 have Z values of c1=18 and c3=16, respectively. The cornersD1 and D2 have Z values of d1=14 and d2=12. The right pixel block 504has a representative Z value of Zr=15. At the intersections C1 and C3,c1>Zr and c3>Zr. At the corners D1 and D2, d1<Zr and d2<Zr, whichsatisfies the relaxed rendering criterion A′. It is thus determined thatthe object 200 has a possibility of being rendered, and the subsequentrasterization process on the external volume 400 is aborted.

As described above, the external volume 400 is rasterized along scanlines while the rendering determination test is performed on each pixelblock. Once it turns out that the relaxed rendering criterion A′ holdsfor any one pixel block, the object 200 is determined to have apossibility of being rendered and the subsequent rasterization processis aborted. If it turns out that the relaxed rendering criterion A′ doesnot hold for any of the pixel blocks, i.e., the rigid culling criterionB′ holds, the object 200 is culled out.

FIG. 8 shows sampling points on which Z test is performed in the processof rasterizing the polygon 402 of the external volume 400. Since the Ztest is performed on the vertexes, intersections, and corners includedin the shaded pixel blocks inside the polygon 402 of the external volume400, the sampling points are those marked with the white circles. Forthe sampling points on a border between pixel blocks, the Z test will beperformed using the representative Z values of all the pixel blocks thatadjoin each other across the border.

[2.3] Updating Representative Z Values of the Reduced Z-Buffer Based onthe Internal Volume

The internal volume 300 is provided for detecting hidden andnon-rendered areas of the other objects that lie behind the object 200,and for updating the reduced Z-buffer 500. To detect non-rendered areasaccurately, all the following requirements must be satisfied.

1. All the rasterized pixels within pixel blocks of the internal volume300 to be rendered must be covered by the rendering data of the internalvolume 300. Here, the pixel block needs not be covered by only a singlepolygon of the internal volume 300 but may be covered by a plurality ofpolygons. If there is any spatial gap in the pixel block, the otherobjects may be seen through the gap. In such cases, the representative Zvalue cannot be updated with the Z values of the internal volume 300.

2. Select one pixel having the largest Z value from among all therasterized pixels in a pixel block of the internal volume 300 to berendered, and update the representative Z value of that pixel block withthe largest per-pixel Z value in the pixel block.

For the foregoing requirement 1, it is difficult to determine whether ornot there is any spatial gap in the pixel block when it is viewed in aunit of pixel, since the reduced Z-buffer 500 contains Z values only ina unit of pixel block in which a plurality of pixels are put together.The Z test according to the present embodiment is intended to make thehidden surface removal process more efficient, and the object maytherefore be determined to be a rendering target in any case where the Ztest is difficult to perform. In view of this, the representative Zvalues of pixel blocks will be updated only if the internal volume 300is rendered across all the pixels within those pixel blocks of thereduced Z-buffer 500. For this purpose, whether or not all the pixelswithin a pixel block of the reduced Z-buffer 500 are covered by aplurality of polygons is determined by the following determinationprocedure.

(1) Provide each edge of each polygon that constitutes the internalvolume 300 with a determination flag that takes a value of 0 or 1.Initialize the determination flags on the respective edges to 0.

(2) Find a terminal edge of the internal volume 300, and set thedetermination flag on the terminal edge to 1. This process is performedby determining whether or not each edge of each polygon of the internalvolume 300 has any adjoining polygon, thereby detecting an edge that hasno other polygon adjoining thereto. The edge having no other polygonsadjoining thereto is a terminal end, and the determination flag on theterminal edge is set to 1. This process can be performed at the stage ofproducing the internal volume 300.

It should be noted that if the internal volume 300 is a solid3-dimensional body, there is no terminal edge that has no other polygonadjoining thereto and therefore the processing (2) of detecting terminaledges can be omitted. If the internal volume 300 has a plate-like shape,there are some terminal edges that have no other polygon adjoiningthereto and therefore the processing (2) of detecting terminal edges isrequired.

(3) Next, find an edge that forms a border when the internal volume 300is projected onto the screen coordinates for rendering, and set thedetermination flag of the edge to 1. This process is performed byobtaining the normal vector of each of the polygons of the internalvolume 300 when projecting the polygon onto the screen coordinates, anddetecting an edge across which the normal vector of the polygon changesfrom a direction passing through the projection plane from the back tothe front to a direction passing through the projection plane from thefront to the back. A forward polygon that can be seen from the point ofview has a normal vector in the direction passing through the projectionplane from the back to the front. A rearward polygon that cannot be seenfrom the point of view has a normal vector in the direction passingthrough the projection plane from the front to the back. Consequently,the edge of the polygon that forms a border when the internal volume 300is rendered can be detected according to the change in the direction ofthe normal vector. The determination flag on the edge that are detectedas a border is set to 1.

(4) The pixel blocks of the reduced Z buffer 500 that the edges passthrough, which are detected to have the determination flag of 1 in theforegoing processing (2) and (3), can possibly have spatial gapstherein, because all the pixels in those pixel blocks are notnecessarily rendered. Therefore, the pixel block that includes at leastone edge having the determination flag of 1 is excluded from the targetfor updating of the representative Z values. The pixel block that onlyedges having the determination flag of 0 pass through is then subject tothe updating of the representative Z values.

Referring to FIGS. 9, 10, and 11A to 11C, a description will be given ofthe foregoing determination procedure (1) to (4). FIG. 9 shows therelationship between projected polygons of the internal volume 300 andthe reduced Z-buffer 500. Among the pixel blocks of the reduced Z-buffer500 that the edges of the polygons of the internal volume 300 passthrough, the shaded pixel blocks alone are subject to the updating ofthe representative Z values. This will be described with reference toFIGS. 10 and 11A to 11C.

FIG. 10 shows the values of the determination flags that are set on therespective edges of the polygons of the internal volume 300 shown inFIG. 9. The edges having the determination flags of 1 are the borders ofthe internal volume 300. FIGS. 11A to 11C shows polygon edges that passthrough the pixel blocks 510, 512, and 514 of the reduced Z-buffer 500of FIG. 9, along with the values of the determination flags of FIG. 10.

As shown in FIG. 11A, an edge 302 having a determination flag of 1 andan edge 304 having a determination flag of 0 pass through the pixelblock 510. Since the edge 302 having the determination flag of 1 is aborder, four pixels 601, 602, 603, and 604 in the pixel block 510 arenot involved in polygon rendering. This produces a spatial gap such thatthe other objects behind can possibly be seen. Thus, the representativeZ value of this pixel block 510 will not be updated.

As shown in FIG. 11B, three edges 306, 308, and 310 having thedetermination flags of 0 pass through the pixel block 512. Since all thepixels of the pixel block 512 are entirely covered with three polygons,there is no spatial gap. The representative Z value of this pixel block512 will therefore be subject to updating.

As shown in FIG. 11C, two edges 316 and 318 having the determinationflag of 0 and two edges 312 and 314 having the determination flag of 1pass through the pixel block 514. Since two pixels 605 and 606 are notinvolved in polygon rendering, there arises a spatial gap such that theother objects behind can possibly be seen. Therefore, the representativeZ value of this pixel block 514 will not be updated.

As described above, the determination flags on the respective edges ofthe polygons shown in FIG. 10 are consulted to identify for which pixelblocks the representative Z values should be updated. FIG. 9 shows theresult in which only the pixel blocks shown shaded are subject to theupdating of the representative Z values. A description will now be givenof the method for updating the representative Z values.

[Z Value Updating Condition C]

For a pixel block of the reduced Z-buffer 500 that is entirely coveredby the internal volume 300, update the representative Z value of thepixel block with the largest per-pixel Z value within the pixel block ifall the rasterized pixels within the pixel block of the internal volume300 to be rendered have the Z value smaller than the representative Zvalue of that pixel block of the reduced Z-buffer 500, or equivalently,update the representative Z value of the pixel block with the largestper-pixel Z value within that pixel block if the largest per-pixel Zvalue within the pixel block of the internal volume 300 to be renderedis smaller than the representative Z value of that pixel block of thereduced Z-buffer 500.

Since the internal volume 300 has flat polygon surfaces, therepresentative Z value Zr of the reduced Z-buffer 500 has only to becompared with the following three types of Z values: the Z value of apixel at a polygon vertex B; the Z value of a pixel at an intersection Cbetween an edge of the polygon and a border of the pixel block; and theZ values of pixels at the four corners D1 to D4 of the pixel block.Consequently, the Z value updating condition C can be simplified asfollows.

[Z Value Updating Condition C′]

For a pixel block of the reduced Z-buffer 500 that is entirely coveredby the internal volume 300, update the Z value of the reduced Z-bufferwith the value of max(b, c, d1, d2, d3, d4) if max(b, c, d1, d2, d3,d4)<Zr. Here, b is the Z value at a polygon vertex B of the internalvolume 300 that falls within the pixel block, c is the Z value at anintersection C between an edge of the polygon and a border of the pixelblock, and d1 to d4 are the Z values at the four corners D1 to D4 of thepixel block. If there are plural vertexes B or intersections C, all thesampling points are subjected to the evaluation.

This Z value updating condition C′ is intended to update the currentrepresentative Z value Zr of the reduced Z-buffer with the Z value ofthe farthest point among the vertex(es) B, the intersection(s) C, andthe four corners D1 to D4 if the farthest point lies closer than therepresentative Z value Zr. The representative Z value is updated onlywhen it is certain that the polygon lies in front, and not updated whenin doubt. When the reduced Z-buffer 500 having the representative Zvalues thus updated is consulted to perform the Z culling test, it isguaranteed that any object having a possibility of being rendered willnever be erroneously culled out.

FIG. 12 explains how the representative Z value of the pixel block 512of the reduced Z-buffer 500 is updated. The pixel block 512 is entirelycovered with the polygons of the internal volume 300, and it is thussubject to updating of the representative Z value. The vertex B of thepolygon 402 has a Z value of b=10. The intersections C1 to C3 have Zvalues of c1=40, C2=30, and c3=30, respectively. The four corner pointsD1 to D4 have Z values of d1=43, d2=42, d3=35, and d4=34, respectively.Since the pixel block 512 has a representative Z value of Zr=48, the Zvalue updating condition C′ is satisfied. The representative Z value Zris updated with the largest Z value of d1=43 that is the Z value at thecorner D1.

FIG. 13 shows sampling points subject to the Z test in rasterizing thepolygons of the internal volume 300. In the shaded pixel blocks forwhich the representative Z values are targeted for updating, the Zvalues of the sampling points shown by white circles are compared withthe representative Z values of the respective pixel blocks. If the Zvalue updating condition C′ is satisfied, the representative Z value ofthat pixel block is updated.

[3] Advantages and Modification of the Embodiment

According to the present embodiment as described, the object 200 isprovided with the external volume 400 and the internal volume 300 anddifferent types of Z tests are performed on the respective volumes usingthe reduced Z-buffer 500. This makes it possible to cull out the object200 that has no possibility of being rendered, thereby enhancing theefficiency of the hidden surface removal processing.

In addition, the object 200 is sandwiched between the external volume400 and the internal volume 300, or double bounding volumes. Theaccuracy with which the double bounding volumes approximate the shape ofthe object 200 can be adjusted to arbitrarily change the cullingefficiency as appropriate.

The conventional methods for generating the reduced Z-buffer includesobtaining an ordinary pixel-by-pixel Z-buffer, and putting together theZ values of a plurality of pixels stepwise so as to generate ahierarchical Z-buffer having resolutions reduced stepwise. According tothe present embodiment, however, the reduced Z-buffer in units of pixelblocks can be directly obtained with high processing efficiency withoutusing the ordinary pixel-by-pixel Z-buffers. The representative Z valuesof the reduced Z-buffer are carefully updated only after it is confirmedthat pixel blocks are entirely covered with object polygons and that thepolygons lie in front. This makes it possible to obtain the reducedZ-buffer causing no damage, without using the pixel-by-pixel Z-buffer.

Various modifications may be made to the foregoing embodiment. Somemodifications will be described below.

[3.1] Front Board and Rear Board

In the foregoing description, an object 200 is provided with doublebounding volumes, i.e., the external volume 400 and the internal volume300. The Z culling test is performed using the external volume 400 whilethe representative Z values of the reduced Z-buffer are updated usingthe internal volume 300. In another embodiment, the double boundingboards consisting of a front board and a rear board may be provided tosandwich the object in the depth direction from the front and the backas seen from the point of view. Here, the front board is used to performthe Z culling test, and the rear board is used to update therepresentative Z values of the reduced Z-buffer.

FIGS. 14A and 14B show a front board 420 and a rear board 320 providedfor the object 200. As shown in FIG. 14A, the front board 420 lies infront of the object 200 so as to hide the object 200 behind as seen fromthe point of view V. The rear board 320 lies behind the object 200 so asto be hidden behind the object 200. When seen from the point of view V,the object 200 is entirely hidden behind the front board 420. The rearboard 320 is entirely hidden behind the object 200. FIG. 14B shows thepositional relationship between the object 200, the front board 420, andthe rear board 320 with respect to the point of view V as seen from thetop.

The front board 420 entirely hides the object 200 as seen from the pointof view V, and thus it provides the same effect as the external volume400 in the Z culling test. The above-mentioned method for the Z cullingtest can therefore be applied to the front board 420. The rear board 320is entirely hidden behind the object 200 as seen from the point of viewV, and thus it provides the same effect as the internal volume 300 whenthe reduced Z-buffer 500 is updated. The above-mentioned method forupdating the representative Z values of the reduced Z-buffer 500 cantherefore be applied to the read board 320.

For example, the front board 420 may be a rectangle having the minimumsize capable of surrounding the entire outline of the object 200projected on the drawing plane. The rear board 320 may be a rectanglehaving the maximum size capable of being entirely surrounded by theoutline of the object 200. Otherwise, the front board 420 and the rearboard 320 may have arbitrary shapes, or may be shaped close to theoutline of the object 200. The closer to the outline of the object 200the front board 420 and the rear board 320 are shaped, the higher theculling efficiency can be. The closer to the object 200 the front board420 and the rear board 320 are placed in front of and behind the object200 respectively, the higher the culling efficiency can be.

In terms of processing cost, it is much easier to generate the frontboard 420 and the rear board 320 for the object 200 than to generate theexternal volume 400 and the internal volume 300 for the object 200. Thefront board 420 and the rear board 320 are also easy to rasterize sothat the Z culling test and updating of the representative Z values ofthe reduced Z-buffer 500 can be performed at high speed.

If the point of view moves, the object 200 could fail to be hiddenbehind the front board 420, or the rear board 320 could be seen behindthe object 200. When the position of the point of view is thus changed,the front board 420 and the rear board 320 will need to be set again. Inthis respect, the external volume 400 and the internal volume 300 remainthe double bounding volumes that confine the object 200 from outside andinside no matter which point of view is taken, and therefore thesevolumes need not be set again even when the point of view moves. Forthis reason, if the point of view moves, it is more preferable to usethe external volume 400 and the internal volume 300.

When the object 200 moves, the external volume 400 and the internalvolume 300 must be rasterized again causing a heavy processing load. Incontrast, the front board 420 and the rear board 320 are easier to setagain even when the object 200 moves, resulting in a less processingload. In such a situation that the object 200 moves frequently, it ismore preferable to use the front board 420 and the rear board 320.

[3.2] Omission of Components

The foregoing embodiment has dealt with the method for providing theobject 200 with double bounding volumes, or the external volume 400 andthe internal volume 300, and approximating the object 200 in the depthdirection and performing a Z culling test while updating the reducedZ-buffer 500. The internal volume 300, which is entirely included insidethe object 200, is used to create the reduced Z-buffer 500, and thereduced Z-buffer 500 is used to perform a culling test based on theexternal volume 400 that entirely includes the object 200. Thisguarantees that the object 200, if it is to be rendered, will never beculled out by mistake.

The occlusion culling method using the reduced Z-buffer 500 and thedouble bounding volumes has the following advantages in terms of memorycapacity and processing load.

(A) Since the bounding volumes in use have less complexities than theactual object 200, it is possible to store the polygon models with asmaller memory capacity, and also rasterize the polygon models at higherspeed.

(B) Since the reduced Z-buffer 500 is used to perform a Z test in unitsof pixel blocks, the required memory capacity and the number ofoperations are smaller as compared to pixel-by-pixel Z test using anordinary Z-buffer.

As some possible modifications of the embodiment, the following methodscan be adopted.

(1) A method for occlusion culling in which the double bounding volumesare rasterized in an ordinary Z-buffer instead of using the reducedZ-buffer 500, or

(2) A method for occlusion culling in which the object 200 is rasterizedin the reduced Z-buffer 500 instead of using the double boundingvolumes.

In other words, the present invention may be practiced even when eitherthe reduced Z-buffer 500 or the double bounding volumes is omitted fromits components.

If the reduced Z-buffer 500 is omitted, the foregoing advantage (B)attributable to implementing the reduced Z-buffer 500 is lost while theforegoing advantage (A) attributable to implementing the double boundingvolumes remains. If the double bounding volumes are omitted, theforegoing advantage (A) attributable to the double bounding volumes islost while the foregoing advantage (B) attributable to the reducedZ-buffer 500 remains. In either case, the objective of occlusion cullingcan still be achieved, while part of the advantages is lost.

Similarly, when the front board 420 and the rear board 320, or doublebounding boards are used, the objective of occlusion culling can also beachieved even if the reduced Z-buffer is omitted from the components.

While the embodiment has dealt with a method for performing culling inunits of objects, the present invention may also be applied whenperforming culling in units of object-constituting fragments such aspolygons. The Z culling using the reduced Z-buffer according to theembodiment is not limited to units of objects, but is also applicable inunits of primitives. In the embodiment the occlusion culling is intendedto select an object that is hidden behind the other objects andinvisible from the point of view and to exclude the object in advancefrom rendering targets. Alternatively, the reduced Z-buffer according tothe embodiment may be used with a hidden surface removal method fordetecting and removing an object surface that is hidden behind the otherobjects, i.e., a hidden surface. The reduced Z-buffer of the embodimentis thus applicable not only to the occlusion culling in units of objectsbut also applicable to the hidden surface removal for removing hiddensurfaces of the objects, resulting in an improvement in the processingefficiency of the Z culling.

Furthermore, various types of rendering processing using a hierarchicalZ-buffer can adopt the reduced Z-buffer of the embodiment instead of thehierarchical Z-buffer. Such a configuration is advantageous in terms ofthe amount of calculation and the memory capacity, because the lowerresolution reduced Z-buffer is directly produced without using apixel-by-pixel Z-buffer, according to the foregoing embodiment.

[4] Configuration of Rendering Processing Apparatus

Hereinafter, a description will be given of the configuration andoperation of a rendering processing apparatus 100 which uses theocclusion culling method according to the foregoing embodiment and itsmodifications. The configuration of the rendering processing apparatus100 will be described with reference to FIGS. 15 to 17. The figure showsa block diagram focused on functions. These function blocks may berealized in various forms such as hardware only, software only, or acombination thereof.

FIG. 15 is a block diagram of the rendering processing apparatus 100according to the embodiment. The rendering processing apparatus 100performs rendering processing for generating rendering data to bedisplayed on a two-dimensional screen based on three-dimensional modelinformation. The rendering processing apparatus 100 is composed of amain processor 130 and a graphics processor 110 which are connected toeach other via an input and output interface 160. The main processor 130uses a main memory 170 for its storage area, and executes arithmeticprocessing such as geometric operations. The graphics processor 110 usesa frame buffer 50 for its storage area, and executes rasterization andrendering processing such as shading algorithm.

The main processor 130 includes a Z culling processing unit 140. Thegraphics processor 110 includes a rendering processing unit 120. Themain processor 130 reads data on a plurality of objects to be renderedfrom an external storage device or the like, and stores them in the mainmemory 170. The Z culling processing unit 140 uses a reduced Z-buffer toperform Z culling processing so that a hidden object behind the otherobjects are excluded from rendering targets. The objects that have apossibility of being rendered are supplied to the graphics processor 110through the I/O interface 160. The rendering processing unit 120rasterizes the objects that have a possibility of being rendered, andthen renders them in the frame buffer 50.

FIG. 16 is a block diagram of the Z culling processing unit 140. Anobject input unit 142 inputs a plurality of objects to be rendered, andstores them in an object storing unit 152 as a set of objects.

An internal volume generating unit 148 generates an internal volume 300that is included inside an input object 200, and supplies it to areduced Z-buffer updating unit 150. Based on the internal volume 300,the reduced Z-buffer updating unit 150 updates the reduced Z-buffer 500stored in a reduced Z-buffer storing unit 154. The process performed bythe reduced Z-buffer updating unit 150 for updating the representative Zvalues of the reduced Z-buffer 500 is the same as described in section[2.3]. The reduced Z-buffer updating unit 150 stores the updated reducedZ-buffer 500 into the reduced Z-buffer storing unit 154.

An external volume generating unit 144 generates an external volume 400that includes the object 200 subject to a culling test, and supplies itto a culling determination unit 146. The culling determination unit 146consults the reduced Z-buffer 500 stored in the reduced Z-buffer storingunit 154, and performs the Z culling test on the object 200 based on theexternal volume 400. The Z culling test performed by the cullingdetermination unit 146 is the same as described in section [2.2]. Theculling determination unit 146 eliminates the object that is excludedfrom rendering targets by Z culling test, from the set of objects storedin the object storing unit 152. The Z culling processing unit 140supplies the set of objects, each having a possibility of being renderedand being stored in the object storing unit 152, to the renderingprocessing unit 120.

FIG. 17 is a block diagram of the rendering processing unit 120. Therendering processing unit 120 includes a rasterizer 10 and a shader 20.The objects that have a possibility of being rendered are input to therasterizer 10. The rasterizer 10 includes a primitive generating unit30, a setup processing unit 32, and a DDA 34.

Based on polygon information on an input object, the primitivegenerating unit 30 generates a stream that contains the vertexcoordinates and parameters of one or more primitives constituting theobject, and supplies the stream to the setup processing unit 32. Aprimitive is a rendering unit in a form of a geometric figure such as apoint, line, triangle, or rectangle used when a three-dimensional objectis represented in a polygonal model.

The setup processing unit 32 sets up various types of parameters forprocessing the stream of primitives with a digital differential analyzer(DDA). Specifically, it sets bounding boxes for defining a spaceincluding the primitives, and various types of DDA processing parameterssuch as edge coefficients.

The setup processing unit 32 supplies the set primitive data to the DDA34. The DDA 34 performs DDA processing on the primitives supplied fromthe setup processing unit 32 based on the various types of parametersset by the setup processing unit 32, thereby converting them into pixeldata corresponding to the drawing screen.

Primitives may have a triangular shape, for example. The DDA 34 performsview conversion for converting triangles in three-dimensional space intotriangles on the drawing plane through projection transformation. TheDDA 34 also scans the drawing plane for triangles in the horizontaldirection of the drawing plane while converting them into quantizedpixels with respect to each raster line. In the DDA 34, primitives aredeveloped into pixels. Pixel data is calculated for each of the pixels,including color values which are expressed in three primary colors RGB,an alpha value which indicates a transparency, a Z value which indicatesa depth, and UV coordinate values which are parametric coordinates foraccessing texture attributes.

The shader 20 performs shading processing to determine the color valuesof the pixels based on the pixel data calculated by the rasterizer 10.When performing further texture mapping, the shader 20 synthesizes thecolor values of textures to calculate the final color values of thepixels, and writes the pixel data to the frame buffer 50.

The shader 20 also performs fogging, alpha-blending, and otherprocessing on the rendering data retained in the frame buffer 50,thereby determining the final color values of the pixels and updatingthe pixel data in the frame buffer 50.

The frame buffer 50 is a buffer in which the pixel data generated by theshader 20 are stored in screen coordinates. The stored pixel data may beeither a final rendering image or an intermediate image in the processof shading processing. The pixel data stored in the frame buffer 50 areoutput to and displayed on a display unit.

In the foregoing description, the Z culling processing unit 140 isprovided in the main processor 130. Since the external volume generatingunit 144 and the internal volume generating unit 148 of the Z cullingprocessing unit 140 rasterize the external volume 400 and the internalvolume 300, respectively, the process could be performed by therasterizer 10 of the rendering processing unit 120. For this reason, theZ culling processing unit 140 may be provided in the graphics processor110 so that each component of the Z culling processing unit 140 can berealized by utilizing the arithmetic functions of the rasterizer 10 andthe shader 20. In this case, multipass rendering techniques may be usedso that the objects that have no possibility of being rendered can beculled out in the first operation pass, and only the objects that have apossibility of being rendered can be input and rendered in thesubsequent operation pass.

FIG. 18 is a flowchart for explaining the procedure of the Z cullingprocessing by the Z culling processing unit 140. The object input unit142 inputs N objects (S1O). The object input unit 142 initializes avariable i for counting the processed objects to zero (S12). The objectinput unit 142 increments the variable i by one (S14), and supplies thei-th object to the external volume generating unit 144 and the internalvolume generating unit 148.

The external volume generating unit 144 generates an external volumewhich includes the i-th object. The internal volume generating unit 148generates an internal volume which is included inside the i-th object(S16).

The culling determination unit 146 performs the Z culling test using thereduced Z-buffer 500, based on the external volume which includes thei-th object (S18). The internal volume generating unit 148 updates thereduced Z-buffer 500 based on the internal volume which is includedinside the i-th object (S20).

If the variable i is smaller than the total number N of objects (Y atS22), the procedure returns to step S14. If the variable i reaches thetotal number N of objects (N at S22), the procedure ends.

In the foregoing procedure, the Z culling test is performed by using theexternal volume which includes the i-th object, and then the reducedZ-buffer 500 is updated using the internal volume which is included inthe i-th object. However, the culling test and the updating of thereduced Z-buffer 500 need not be performed in this order since they canbe executed independently. Moreover, all the objects need notnecessarily be subject to both the Z culling test and the updating ofthe reduced Z-buffer 500. One set of objects may be used for updatingthe reduced Z-buffer 500 while another different set of objects may besubject to Z culling test.

For example, the reduced Z-buffer 500 may be updated for the objectshaving a larger size or for the objects known beforehand to lie infront, while the objects having a smaller size or the objects knownbeforehand to lie behind may be omitted as appropriate. It can help areduction in the processing cost.

The objects subject to Z culling test may also be selected asappropriate. For example, the culling test may be performed withpriority given to the objects known beforehand to lie behind, or with afocus on the objects that are heavy to process.

FIG. 19 is a flowchart showing the procedure of culling test performedby the culling determination unit 146 at step S18. The cullingdetermination unit 146 rasterizes the external volume of the object(S30), and identifies M pixel blocks in which the external volume isrendered (S32). A variable j for counting the processed pixel blocks isinitialized to zero (S34).

The variable j is incremented by one (S36). If it turns out that one ofpixels of the external volume in the j-th pixel block has a Z valuesmaller than the representative Z value of this pixel block (Y at S38),the culling determination unit 146 determines not to perform culling(S40) since this object has a possibility of being rendered.

If none of the pixels of the external volume in the j-th pixel block hasa Z value smaller than the representative Z value of the pixel block (Nat S38), the culling determination unit 146 does not determine that theobject is a rendering target for this pixel block. If the variable j issmaller than the total number M of pixel blocks (Y at S42), theprocedure returns to step S36 to continue the Z test on the rest of thepixel blocks. Finally, if it turns out that all the pixels of theexternal volume for all of the M pixel blocks have Z values greater thanor equal to the representative Z values of the respective pixel blocks(N at S38 and N at S42), the culling determination unit 146 performsculling (S44) since this object has no possibility of being rendered.

The culling test ends when it is determined whether or not to cull outthe object (S40 or S44).

FIG. 20 is a flowchart showing the procedure performed by the reducedZ-buffer updating unit 150 for updating the reduced Z-buffer 500 at stepS20. The reduced Z-buffer updating unit 150 rasterizes the internalvolume of the object (S50), and identifies L pixel blocks as beingcovered by the polygons of the internal volume (S52). A variable k forcounting the processed pixel blocks is initialized to zero (S54).

The variable k is incremented by one (S56). If the largest per-pixel Zvalue within the k-th pixel block is smaller than the representative Zvalue of this pixel block (Y at S58), the reduced Z-buffer updating unit150 updates the representative Z value with the largest per-pixel Zvalue (S60). If the variable k is smaller than the total number L ofpixel blocks (Y at S62), the procedure returns to step S56 to performthe Z test on the rest of the pixel blocks. If the variable k reachesthe total number L of pixel blocks (N at S62), the procedure ends.

If the largest per-pixel Z value within the k-th pixel block is greaterthan or equal to the representative Z value of this pixel block (N atS58), the reduced Z-buffer updating unit 150 does not update therepresentative Z value and the procedure proceeds to step S62.

The present invention has been described in conjunction with theembodiment thereof. The foregoing embodiment has been given solely byway of illustration. It will be understood by those skilled in the artthat various modifications may be made to combinations of the foregoingcomponents and processes, and all such modifications are also intendedto fall within the scope of the present invention.

1. A reduced Z-buffer generating method comprising: providing a reducedZ-buffer which contains representative Z values for determining apositional relationship between plural objects or fragments constitutingthe objects in a depth direction, the representative Z values indicatinga depth from the point of view in units of predetermined pixel blockseach including a plurality of neighboring pixels; and comparing the Zvalues of respective rasterized pixels in a pixel block of an object ora fragment to be rendered with the representative Z value of acorresponding pixel block stored in the reduced Z-buffer, and updatingthe representative Z value of the pixel block with a farthest Z value ifthe farthest Z value indicates lying closer to the point of view thanthe representative Z value of the pixel block does, the farthest Z valueindicating lying the farthest from the point of view among the per-pixelZ values in the pixel block.
 2. The reduced Z-buffer generating methodaccording to claim 1, wherein the representative Z value of the pixelblock in the reduced Z-buffer is updated only if the object or thefragment is rendered on all the pixels within the pixel block.
 3. Thereduced Z-buffer generating method according to claim 2, wherein whencomparing the Z values of the rasterized pixels in the pixel block ofthe object or fragment to be rendered with the representative Z value ofthe corresponding pixel block stored in the reduced Z-buffer, therepresentative Z value is compared with: a Z value of a pixel at avertex of a polygon of the object or fragment falling within the pixelblock; a Z value of a pixel at an intersection between an edge of thepolygon and a border of the pixel block; and Z values of pixels at fourcorners of the pixel block.
 4. An occlusion culling method for excludingfrom rendering targets a hidden object behind another objects as seenfrom a point of view, when given a plurality of objects, the methodcomprising: providing a reduced Z-buffer which contains representative Zvalues for determining a positional relationship between the objects ina depth direction, the representative Z values indicating a depth fromthe point of view in units of predetermined pixel blocks each includinga plurality of neighboring pixels; comparing the Z values of respectiverasterized pixels in a pixel block of an object to be rendered with therepresentative Z value of a corresponding pixel block stored in thereduced Z-buffer, and updating the representative Z value of the pixelblock with a farthest Z value if the farthest Z value indicates lyingcloser to the point of view than the representative Z value of the pixelblock does, the farthest Z value indicating lying the farthest from thepoint of view among the per-pixel Z values in the pixel block; anddetermining that the object has a possibility of being rendered if itturns out that at least one of the pixel blocks of the object to berendered has any rasterized pixel having a Z value that indicates lyingcloser to the point of view than the representative Z value of acorresponding pixel block stored in the Z-buffer does.
 5. The occlusionculling method according to claim 4, wherein the object is excluded fromrendering targets if for every pixel block of the object to be rendereda most significant per-pixel Z value, which indicates lying closest tothe point of view among the per-pixel Z values in the every pixel block,indicates lying farther from the point of view than the representative Zvalue of the corresponding pixel block stored in the reduced Z-bufferdoes.
 6. The occlusion culling method according to claim 5, wherein whencomparing the per-pixel Z values in a pixel block of the objects to berendered with the representative Z value of the corresponding pixelblock stored in the reduced Z-buffer, the representative Z value iscompared with: a Z value of a pixel at a vertex of a polygon of theexternal volume falling within the pixel block; a Z value of a pixel atan intersection between an edge of the polygon and a border of the pixelblock; and a Z value of a pixel at a corner falling within the polygonamong four corners of the pixel block.
 7. A hidden surface removalmethod for removing a hidden surface behind another object as seen froma point of view, when given a plurality of objects, the methodcomprising: providing a reduced Z-buffer which contains representative Zvalues for determining a positional relationship between fragmentsconstituting the plurality of objects in a depth direction, therepresentative Z values indicating a depth from the point of view inunits of predetermined pixel blocks each including a plurality ofneighboring pixels; comparing the Z values of respective rasterizedpixels in a pixel block of a fragment to be rendered with therepresentative Z value of a corresponding pixel block stored in thereduced Z-buffer, and updating the representative Z value of the pixelblock with a farthest Z value if the farthest Z value indicates lyingcloser to the point of view than the representative Z value of the pixelblock does, the farthest Z value indicating lying the farthest from thepoint of view among the per-pixel Z values in the pixel block; anddetermining that the fragment has the possibility of being rendered ifit turns out that at least one of the pixel blocks of the fragment to berendered has any rasterized pixel having a Z value that indicates lyingcloser to the point of view than the representative Z value of acorresponding pixel block stored in the Z-buffer does.
 8. The hiddensurface removal method according to claim 7, wherein the fragment isexcluded from rendering targets if for every pixel block of the fragmentto be rendered a most significant per-pixel Z value, which indicateslying closest to the point of view among the per-pixel Z values in theevery pixel block, indicates lying farther from the point of view thanthe representative Z value of the corresponding pixel block stored inthe reduced Z-buffer does.